11.2: Surface Area of Prisms and Cylinders

Learning Objectives

Review Queue

Find the area of a rectangle with sides:

6 and 9

11 and 4

and

If the area of a square is , what are the lengths of the sides?

If the area of a square is , what are the lengths of the sides?

Know What? Your parents decide they want to put a pool in the backyard. The shallow end will be 4 ft. and the deep end will be 8 ft. The pool will be 10 ft. by 25 ft. How much siding do they need to cover the sides and bottom of the pool?

Parts of a Prism

Prism: A 3-dimensional figure with 2 congruent bases, in parallel planes, and the other faces are rectangles.

The non-base faces are lateral faces.

The edges between the lateral faces are lateral edges.

This is a pentagonal prism.

Right Prism: A prism where all the lateral faces are perpendicular to the bases.

Oblique Prism: A prism that leans to one side and the height is outside the prism.

Surface Area of a Prism

Surface Area: The sum of the areas of the faces.

Lateral Area: The sum of the areas of the lateral faces.

Example 1: Find the surface area of the prism below.

Solution: Draw the net of the prism.

Using the net, we have:

Surface Area of a Right Prism: The surface area of a right prism is the sum of the area of the bases and the area of each rectangular lateral face.

Example 2: Find the surface area of the prism below.

Solution: This is a right triangular prism. To find the surface area, we need to find the length of the hypotenuse of the base because it is the width of one of the lateral faces.

Looking at the net, the surface area is:

Cylinders

Cylinder: A solid with congruent circular bases that are in parallel planes. The space between the circles is enclosed.

A cylinder has a radius and a height.

A cylinder can also be oblique, like the one on the far right.

Surface Area of a Right Cylinder

Let’s find the net of a right cylinder. One way to do this is to take the label off of a soup can. The label is a rectangle where the height is the height of the cylinder and the base is the circumference of the circle.